Finite Group Databasebeta

← #25249151

Subgroups — #25249151

Order 11008.

1618 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583289C212yesmaximal, complemented
2C2×#14583285C214yesmaximal, complemented
3C2×#14583284C212yesmaximal, complemented
4C2×#14583276C211yesmaximal, characteristic, complemented
5C2×#14583274C212yesmaximal, complemented
6#19140703C212yesmaximal, complemented
7#19134281C211yesmaximal, characteristic, complemented
8C2×C43×#495C211yesmaximal, characteristic, complemented
9C22×#10621884C2214yes—
10C22×D344C2212yes—
11C22×D344C2212yes—
12C22×#10621882C2214yes—
13C2×#13063322C2212yes—
14C2×#13063321C2214yes—
15C2×#13063314C2214yes—
16#14583289—28no—
17#14583285—216no—
18#14583284—28no—
19#14583276—24no—
20#14583274—28no—
21C2×#13063236C2211yescharacteristic
22C2×#13063235C2212yes—
23C2×C8×Dic43C2212yes—
24#14582808—28no—
25#14582745C2211yescharacteristic
26C22×Q16×C43C2211yescharacteristic
27C22×SD16×C43C2212yes—
28C22×D8×C43C2211yescharacteristic
29C2×#124×C43C2212yes—
30C43×#495—24no—
31C2×C4×C8×C43C2211yescharacteristic
32C22×D172—24no—
33C22×D172C2314yes—
34C22×C22⋊D43—28no—
35C2×#10621884—28no—
36C2×#10621884—28no—
37C2×#10621884—28no—
38C2×D344—24no—
39C2×D344—24no—
40C2×D344—24no—
41C2×D344—24no—
42C2×D344—28no—
43C2×#10621882—28no—
44C2×#10621882—28no—
45C2×#10621882—28no—
46C22×C43⋊C8C2312yes—
47#13063322—24no—
48#13063322—24no—
49#13063321—28no—
50#13063321—28no—
51#13063314—28no—
52#13063314—28no—
53C2×(C2×D43)⋊C4—28no—
54C2×C4×Dic43C2312yes—
55#13063236D414yescomplemented
56#13063235D418yescomplemented
57C8×Dic43D418yescomplemented
58C43⋊#95D414yes—
59C22×Q8×C43C2312yes—
60C22×D4×C43C2312yes—
61C2×Q16×C43—24no—
62C2×Q16×C43—22no—
63C2×SD16×C43—28no—
64C2×SD16×C43—24no—
65C2×D8×C43—24no—
66C2×D8×C43—22no—
67C22×C8×C43C2311yescharacteristic
68C22×C8×C43C2311yescharacteristic
69#124×C43—24no—
70#124×C43—24no—
71C2×C22⋊C4×C43—24no—
72C2×C42×C43C2311yescharacteristic
73C4×C8×C43D414yescomplemented
74C24×C43—22no—
75C23×D43—24no—
76C2×Q8×C43—22no—
77C2×Q8×C43—22no—
78C2×Q8×C43—24no—
79C2×Q8×C43—24no—
80C2×D4×C43—22no—
81C2×D4×C43—22no—
82C2×D4×C43—24no—
83C2×D4×C43—24no—
84C22×C4×C43—22no—
85C22×C4×C43C2×D412yes—
86C22×C4×C43C2411yescharacteristic
87C2×C22⋊D43—416no—
88C2×C22⋊D43—816no—
89C22×Dic43C2×D414yes—
90C2×D172—24no—
91C2×D172—24no—
92C2×D172—24no—
93C2×D172—24no—
94C2×D172—24no—
95C2×D172—24no—
96C2×D172—48no—
97C2×D172—88no—
98Q16×C43—44no—
99SD16×C43—48no—
100D8×C43—44no—
101C2×C8×C43C2×D414yes—
102C2×C8×C43C2×D414yes—
103C2×C8×C43C2×D412yes—
104C2×C8×C43C2×D412yes—
105C22⋊C4×C43—48no—
106C42×C43C2×D412yes—
107C42×C43C2×D412yes—
108#10621884—416no—
109#10621882—416no—
110(C2×D43)⋊C4—416no—
111C4×Dic43C2×D414yes—
112C4×Dic43C2×D414yes—
113C2×C43⋊C8C2×D414yes—
114C2×C43⋊C8C2×D414yes—
115C2×C43⋊C8C2×D414yes—
116D344—48no—
117D344—48no—
118C23×C43—42no—
119C23×C43—44no—
120C23×C43—48no—
121C23×C43C22×D411yescharacteristic
122C22×D43—44no—
123C22×D43—44no—
124C22×D43—44no—
125C22×D43—416no—
126Q8×C43—44no—
127Q8×C43—42no—
128Q8×C43—42no—
129D4×C43—44no—
130D4×C43—42no—
131D4×C43—42no—
132C2×C4×C43—24no—
133C2×C4×C43—44no—
134C2×C4×C43—42no—
135C2×C4×C43#12714yes—
136C2×C4×C43C22×D411yescharacteristic
137C2×C4×C43C22×D412yes—
138C2×C4×C43C22×D412yes—
139C2×C4×C43C22×D411yescharacteristic
140C22⋊D43—832no—
141C2×Dic43—28no—
142C2×Dic43#12718yes—
143D172—44no—
144D172—44no—
145D172—44no—
146D172—44no—
147D172—816no—
148C8×C43#12714yes—
149C8×C43#12714yes—
150C43⋊C8#12718yes—
151#33308—431nomaximal, Sylow
152C22×C43—82no—
153C22×C43—84no—
154C22×C43—88no—
155C22×C43C2×#12712yes—
156C22×C43C2×#12711yescharacteristic
157C22×C43#57614yes—
158C2×D43—84no—
159C2×D43—88no—
160C2×D43—88no—
161C2×D43—88no—
162C4×C43—24no—
163C4×C43—82no—
164C4×C43C2×#12712yes—
165C4×C43C2×#12711yescharacteristic
166C4×C43C2×#12711yescharacteristic
167Dic43—28no—
168C2×#496—434no—
169C2×#496—432no—
170C2×#495—432no—
171C2×#495D4311yescharacteristic, complemented
172C2×#493—431no—
173C2×#493—432no—
174#2657—432no—
175#1726—431no—
176C2×C43—162no—
177C2×C43#286711yescharacteristic
178C2×C43#315514yes—
179C2×C43#315512yes—
180D43—164no—
181C22×Q16C2×D4311yescharacteristic
182C22×SD16—434no—
183C22×SD16C2×D4312yes—
184C22×D8—434no—
185C22×D8—432no—
186C22×D8—432no—
187C22×D8C2×D4311yescharacteristic
188C2×#127—434no—
189C2×#127—432no—
190C2×#124—434no—
191C2×#124C2×D4312yes—
192#496—868no—
193#496—8616no—
194#495—24no—
195#495—868no—
196#493—868no—
197#493—864no—
198C2×#97—432no—
199C2×#97—431no—
200C2×C4×C8—432no—
201C2×C4×C8C2×D4311yescharacteristic
202#392—868no—
203#376—431no—
204C43#3330811yescharacteristic, complemented, Sylow
205C22×Q8C22×D4312yes—
206C22×D4—434no—
207C22×D4—868no—
208C22×D4—864no—
209C22×D4C22×D4312yes—
210C2×Q16—24no—
211C2×Q16—22no—
212C2×SD16—28no—
213C2×SD16—24no—
214C2×SD16—868no—
215C2×SD16—868no—
216C2×SD16—868no—
217C2×D8—24no—
218C2×D8—22no—
219C2×D8—868no—
220C2×D8—868no—
221C2×D8—868no—
222C2×D8—864no—
223C2×D8—864no—
224C2×D8—868no—
225C2×D8—864no—
226C2×D8—864no—
227C22×C8—432no—
228C22×C8C22×D4311yescharacteristic
229C22×C8C22×D4311yescharacteristic
230#127—868no—
231#127—868no—
232#127—864no—
233#127—864no—
234#124—24no—
235#124—24no—
236#124—868no—
237#124—868no—
238C2×C22⋊C4—24no—
239C2×C22⋊C4—868no—
240C2×C42—432no—
241C2×C42C22×D4311yescharacteristic
242#97—438no—
243#97—434no—
244C4×C8—438no—
245C4×C8C22⋊D4314yescomplemented
246#95—434no—
247C24—22no—
248C24—864no—
249C2×Q8—22no—
250C2×Q8—24no—
251C2×Q8—24no—
252C2×Q8—22no—
253C2×D4—22no—
254C2×D4—24no—
255C2×D4—24no—
256C2×D4—22no—
257C2×D4—864no—
258C2×D4—864no—
259C2×D4—864no—
260C2×D4—864no—
261C2×D4—864no—
262C2×D4—864no—
263C2×D4—3448no—
264C2×D4—34416no—
265C2×D4—17216no—
266C2×D4—1728no—
267C22×C4—22no—
268C22×C4—434no—
269C22×C4D4×D4312yes—
270C22×C4C23×D4311yescharacteristic
271Q16—44no—
272SD16—48no—
273SD16—17216no—
274D8—44no—
275D8—17216no—
276D8—1728no—
277D8—1728no—
278C2×C8—434no—
279C2×C8—434no—
280C2×C8—434no—
281C2×C8D4×D4314yes—
282C2×C8D4×D4314yes—
283C2×C8C2×C22⋊D4312yes—
284C2×C8C2×C22⋊D4312yes—
285C22⋊C4—48no—
286C22⋊C4—17216no—
287C42—434no—
288C42—434no—
289C42D4×D4312yes—
290C42C2×C22⋊D4312yes—
291C23—44no—
292C23—42no—
293C23—48no—
294C23—1724no—
295C23—1724no—
296C23—1724no—
297C23—17216no—
298C23C2×D4×D4311yescharacteristic
299Q8—44no—
300Q8—42no—
301Q8—42no—
302D4—44no—
303D4—42no—
304D4—42no—
305D4—34416no—
306D4—34432no—
307D4—1724no—
308D4—1724no—
309D4—1724no—
310D4—1724no—
311C2×C4—24no—
312C2×C4—44no—
313C2×C4—42no—
314C2×C4—438no—
315C2×C4—868no—
316C2×C4#1306332114yes—
317C2×C4C2×D4×D4311yescharacteristic
318C2×C4C2×D4×D4312yes—
319C2×C4C2×D4×D4312yes—
320C2×C4C22×C22⋊D4311yescharacteristic
321C8—438no—
322C8#1306332114yes—
323C8#1306332114yes—
324C22—82no—
325C22—88no—
326C22—84no—
327C22—3444no—
328C22—3448no—
329C22—3448no—
330C22—3448no—
331C22#127×D4312yes—
332C22C2×#1306332111yescharacteristic
333C22#1458370114yes—
334C4—24no—
335C4—82no—
336C4—868no—
337C4#127×D4312yes—
338C4C2×#1306332111yescharacteristic
339C4C2×#1306332111yescharacteristic
340C2—162no—
341C2—6884no—
342C2#1914298911yescharacteristic
343C2#1914507714yes—
344C2#1914508212yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#495C2
socleC23×C43C22×D4
hypercenterC2×#495D43
hypocenterC43#33308
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#495

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14583289C2semidirect
2. C2×#14583285C2semidirect
3. C2×#14583284C2semidirect
4. C2×#14583276C2semidirect
5. C2×#14583274C2semidirect
6. #19140703C2semidirect
7. #19134281C2semidirect
8. C2×C43×#495C2semidirect
55. #13063236D4semidirect
56. #13063235D4semidirect
57. C8×Dic43D4semidirect
73. C4×C8×C43D4semidirect
171. C2×#495D43semidirect
204. C43#33308semidirect
245. C4×C8C22⋊D43semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145832892
C2×#145832852
C2×#145832842
C2×#145832762
C2×#145832742
#191407032
#191342812
C2×C43×#4952
#3330843